Part I: Structures of Thought
Part I Structures of Thought Passage 1 On Natural Science, Mathematics, and Metaphysics
Source: Thomas's commentary on chapter 2 of Boethius' De Trinitate (incorporating questions 5 and 6). Text from the critical edition of Thomas's original manuscript: Expositio super Librum
Boethii de Trinitate, ed. B. Decker, 2nd edn. (Leiden, 1959), with some corrections from the future Leonine editor, published in Bulletin
Thomiste, 11.54, pp. 4 1 -4 .
Date: Between 1255 and 1259, first stay in Paris, aged 3 0 -4 .
Type of passage: Textual commentary with appended disputed questions (see Introduction).
How to read: The initial section (in italics) is Boethius' text; the second section Thomas's textual commentary into which are woven
Boethius' actual words, picked out in italics; the third section collects together questions raised by Boethius' text, each having the struc ture of a disputed question (see Introduction). Each disputed ques tion consists of four sections (here headed in bold): first, the It seems. . . marshalling many arguments that cast doubt on what
Boethius says (the translation omits some of these arguments); second, the But against that, which rather more briefly collects authorities in support of Boethius' point; third, the In reply, which is Thomas's extensive argument meant to decide the point; and fourth, the Hence, which answers the opening arguments of the question in order. In one case— Question 6, Article 1— the struc ture is more complex: three doubts are cast in the one article (I have labelled them Queries) and the three doubts are first raised by way of a thrice-repeated It seems and But against that, and then answered by a thrice-repeated In reply and Hence.
[Boethius' text. Chapter 2] Come then, let us enter into each matter, discussing1 it so it
Structures of Thought can be grasped and understood, for it seems well said that educated people try for such certainty as the matter itself allows.
For since theoretical science divides into three— natural science, changing, non-abstract, unseparated: which considers bodily forms as forms-in-matter, forms that cannot exist separated from bodies that are changing— like falling earth or rising fire— so that what changes is the form-in-matter; mathematics, changeless, non-abstract: which conceives bodily forms apart from matter and thus from change, though those forms exist in matter and so cannot be separated from matter and change; theology, changeless, abstract, and inseparable:2 for God's being lacks both matter and change— in natural science we make use of reason, in mathematics discipline, in divine science intellect, not relying on imagina tion but rather scrutinizing Form itself [true form and no image. Existence itself from which all existence exists].
[Thomas's explanation of the text] Having already set out Catholic belief in the unity of a threeperson God and given the ground for that belief, Boethius now wants to start investigating these matters; but, guided by Aristotle's opinion3 that before starting a science we must investigate the ways of that science, he proceeds in two steps, first showing the proper way to investigate divine matters, and then, at true form and no image, pursuing his investiga tion in that way. In the first step he first says why we must know the way to investigate, and then, at For since theoret ical science divides, shows the way best suited to the present investigation.
So he says: Come— exhorting us— then, given that Catholics believe in the unity of a three-person God on the ground of undifferentiation, let us enter into each matter, that is, delve within, into the innermost principles of things, penetrating to the truth that lies veiled as it were and hidden; and do this in the proper way, which is why he adds: discuss-
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ing each so it can be grasped and understood, that is, in such a way that it can be grasped and understood. He uses these two verbs since the way things are discussed must suit both the things and ourselves: the things if they are to be under stood, ourselves if we are to grasp them. For example, the divine, of its nature, can be known only by intellect: so those who try to grasp it using imagination won't understand it since the thing itself isn't understandable that way; whereas those who try to see it in itself with the sort of certainty and comprehensiveness with which we comprehend what our senses experience or mathematics can prove, won't get a grasp of it that way, since, however much4 it itself is open to such understanding, our understandings are not up to it.
That there is a proper way of conducting each investiga tion he proves by citing the beginning of Aristode's Ethics, continuing: for it seems well said, namely, by Aristotle, that educated people try for such certainty as the matter itself allows, that is, as the way of approach suited to the matter allows. For not all matters allow the same certainty and clarity of demonstration. Aristotle's actual words5 are: 'It is the mark of an educated person to require as much certainty in a particular domain as the nature of the matter allows.'
Next, when he says: For since theoretical science divides into three, he begins to distinguish the way this investigation should be conducted from ways used by other sciences. And because the way must suit the subject-matter under con sideration he first classifies the sciences by subject-matter, and then, at in natural science, describes the way each should be conducted. The classification proceeds in three steps: first he points out the subject-matter of natural science; then, at mathematics, that of mathematics; and finally, at theology, that of divine science.
So, given that it seems well said that we should try for such certainty as the matter itself allows, he says: For since theoretical science, that is to say, philosophy, as distinct from ethics, which is practical and concerned with action, divides into three, each branch needs to be conducted in a way suited to its subject-matter. The three branches referred to are physical or natural science, mathematics, and theology or
Structures of Thought divine science. Since, to repeat, there are these three: natural science—one of them— is changing, non-abstract, that is, considers things which change, un-abstracted from matter; and this he proves by example as seen in the text. But his phrase what changes is the form-in-matter needs interpreta tion: either it means that what changes as such is the thing itself, composed of matter under this form, or that what gives rise to the change is the form itself, existing in the matter; so that considering bodies as material or as changing amounts to the same thing.
Next he explains mathematics' subject-matter: mathematics is changeless, that is, doesn't consider change and changing things (in this regard differing from natural science), non abstract, that is, concerned with forms that never exist in abstraction from matter (in this regard agreeing with natural science). How this can be he explains: which, namely, mathematics, conceives bodily forms apart from matter and thus from change (for as Aristotle proves,6 wherever there is change there is matter corresponding to the change); so that the mathematician's way of looking at forms is free from matter and change, though those forms, namely, the forms mathematics looks at, exist in matter and so cannot be separated— in their existence— from matter and change. So they can be separated from matter conceptually but not in actual fact.
Next he points out divine science's subject-matter: theology, that is, the third branch of theoretical science, called also divine science or metaphysics or first philosophy, is changeless, in this regard agreeing with mathematics and differing from natural science, abstract, that is, from matter, and inseparable, in these two regards differing from mathematics.
For the divine actually exists abstracted from matter and change whereas mathematical objects exist unabstracted; mathematical objects, however, are separable conceptually whereas the divine is inseparable since only what is joined can be separated.7 So the divine is not conceptually separable from matter but is actually abstracted from matter: the exact opposite of the mathematical case. For proof he refers to God's being, the principal subject-matter of divine science from which its name derives.
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Next, when he says in natural science he points out the ways in which each branch of science should be conducted: firstly, summarizing the ways suited to each branch (and this part of our explanation we will leave to the disputation that follows), and secondly, expanding the last way which is the one proper to the present investigation. Here he first clears away an obstacle, saying: not relying on imagination, that is, not using imagination to judge the way divine matters are; and then, secondly, he points out the proper way: but rather scrutinizing Form itself without matter and without change, the Form whose conditions he treats later when he actually enters on his proposed investigation.
[Questions raised by Thomas in connection with the text] Here two questions need debate: the branches into which the text divides theoretical science; and the different methods of approach ascribed to those branches.
[Question 5] The first question [the branches into which the text divides theoretical science] divides into four:
Is the division of theoretical science into natural, math ematical, and divine science acceptable?
Is natural philosophy concerned with changing material things?
Does mathematics see the material things it is concerned with in an unchanging and immaterial way?
Is divine science concerned with immaterial unchanging things?
[Article 1] The first question [Is the division of theoretical science into natural, mathematical, and divine science acceptable?] we approach as follows:
The division of theoretical science into these branches seems unacceptable:
For [1] the branches of theoretical science are meant to dispose and perfect our mind's ability to see and understand things. But Aristotle8 says our mind's capability of science— its theoretical part— is perfected by the three dispositions
Structures of Thought of wisdom, science, and understanding. These then should be the three branches of theoretical science and not those proposed in the text.
Moreover, [2] Augustine9 says logic, the science of reason, is a branch of theoretical or contemplative science. A classifica tion which makes no mention of logic is therefore defective.
Moreover, [3] people usually divide philosophy into the seven liberal arts, which include no natural or divine science, but only logic and mathematics. So natural and divine science should not be counted as branches of theoretical science.
Moreover, [4] of all sciences medicine seems the most prac tical, yet it has a theoretical as well as a practical part. For the same reason then every other practical science has its theoretical part, and mention should have been made in the classification of ethics or moral science— though practical— because of its theoretical part.
Moreover, [5] medical science, and certain other mechanical [= non-liberal] arts like agriculture, metallurgy, etc., are parts of natural science. Since these are practical sciences it seems natural science can't be classed simply as theoretical.
Moreover, [6] a whole shouldn't be classified alongside its parts. Now divine science seems to be a whole with natural science and mathematics as parts, since its subject-matter includes theirs. For, as first philosophy, its subject-matter is being, and that, as Aristode makes clear,10 includes changing substances— the subject-matter of natural science— and quantity— the subject-matter of mathematics. So divine science shouldn't be classified alongside natural science and mathematics...
Moreover, [9] sciences presupposed to others should rank before them. Now all other sciences presuppose divine sci ence, submitting their first principles to its judgements.
Divine science then should head the list of sciences.
Moreover, [10] mathematics is learnt before natural science, because, as Aristotle points out,11 even children can learn it easily, whereas natural science demands advanced study.
Natural Science, Mathematics, Metaphysics
And so in olden days, we are told, the sciences were learnt in this order: logic, mathematics, natural science, ethics, and finally divine science. Mathematics then should be listed before natural science, and the classification given here seems defective.
But against that:
[1] That this is an acceptable classification we have on Aristotle's authority:12 So theoretical philosophy has three branches: mathematics, natural science, and theology.
Moreover, [2] the three modes of scientific thought men tioned by Aristotle in the Physics13 seem also to be these three.
Moreover, [3] Ptolemy14 too uses this classification.
In reply:
Speculative or theoretical, as distinct from operative or prac tical, understanding is characterized by attention to truth for its own sake, rather than as the means to some other activity.
Aristotle15 calls this a distinction of goal, 'the goal of theo retical understanding being truth but of practical understand ing action'.16 Now since subject-matter must match goal, the subject-matter of practical sciences has to be things we can make or do, which we can be seeking to know for activity's sake, so to say. The subject-matter of theoretical sciences, on the other hand, has to be things not made by us, which we can't be seeking to know for activity's sake; and differences between things of this sort will differentiate theoretical sciences.
But we must remember that when abilities and dispositions are differentiated by the objects they bear on, not any and every difference in object is relevant, but only differences that affect the way objects are objects. Whether an object of our senses is animal or plant is irrelevant to its ability to be sensed, and so we don't differentiate the senses by such a difference, but rather by the difference between colour and sound. We must differentiate speculative sciences then by differences relevant to objects of speculation precisely as such.
Structures of Thought
Now to be an object of our ability to speculate a thing must suit both our basic ability to understand and that further disposition to know things with certainty which perfects our understanding with science. The ability to understand, being itself non-material, requires its objects to be non-material; and the disposition to science requires its objects to be necessary—since we can know with certainty only what must be so.17 What must be so is, as such, un changing, since what changes, as such, can be or not be— exist or not exist in the unqualified sense, or be or not be the way it is.18 Any objects of speculation or theoretical science, then, must, as such, position themselves in relation to matter and change, and according to their degrees of distance from matter and change such objects will determine different theoretical sciences.
Some objects of our speculation, then, depend on matter for their existence, unable to exist except in matter. But a distinction is possible. Some depend on matter not only for existence but also for understanding: since 'perceptible matter' is included in their definition they can't be under stood without that perceptible matter. Thus flesh and bone are included in the definition of human being. Such things are studied by physics, or natural science. Other things depend on matter for existence but not for understanding, since 'perceptible matter' is not included in their definition: things like lines and numbers. And such things are studied by mathematics. Then there are other objects of speculation which don't depend for their existence on matter and are able to exist out of matter, either never existing in matter, like God and the angels, or sometimes existing in matter but sometimes not, like substance, qualities, potentiality and actuality, the one and the many, etc. All such things are studied by theology— science of the divine— so-called because God is its prime object of study. But it is also called metaphysics— 'after-physics'— because we learn it after physics, only able to reach what can't be sensed through what can. And again it is called first philosophy, since all other sciences come after it in the sense of deriving their first principles from it. But because nothing can depend on matter
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for understanding and not for existence— understanding being as such immaterial— no fourth division of philosophy exists beside the ones mentioned.
Hence: to 1: In the Ethics19 Aristode is inquiring about mental dispositions as virtues [or strengths], called that because of their perfecting activity: a virtue renders its possessor and his activity good.20 So he distinguishes these virtues according to their different ways of perfecting and strengthening. The way our speculating mind is strengthened by understanding— disposing us to recognize the self-evident truths which serve as first premisses of our thought— differs from the way we know conclusions deducible from those principles, whether the deduction be from low-level causes, as in science, or from the highest-level ones, as in wisdom. But when we are dis tinguishing sciences as dispositions we must distinguish them with reference to their objects or subject-matters. And that is the way the three branches of theoretical science are dis tinguished here and by Aristotle.21 to 2: As Aristotle makes clear,22 theoretical science concerns itself with anything we seek to know for its own sake. But what logic deals with is not sought for its own sake, but as a support to the other sciences. So logic is not classified as a major branch of theoretical science, but as something that serves philosophy, providing it with tools of speculation: the syllogisms and definitions we need in the theoretical sciences.
That is why Boethius23 calls it not so much a science as a scientific instrument. to 3: The seven liberal arts don't cover all theoretical philo sophy, but according to Hugh of St Victor24 other sciences were left out and these seven collected together because they constitute the first steps in learning philosophy, and so are themselves divided into the three-ways (the trivium) and the four-ways (the quadrivium), pathways by which an alert spirit can enter philosophy's secret places. This agrees with Aristotle's opinion25 that before tackling science one must learn its methods, on which Ibn Rushd commented that logic, since it teaches the method of every science, must be
Structures of Thought learnt before all other sciences (hence the trivium)-, and since
Aristotle26 also said that children can learn mathematics but haven't enough experience for natural science, we can deduce that mathematics should follow on logic (hence the quadrivium). By these then, as by pathways, we prepare our spirit for the other philosophical disciplines. Alternatively, these sciences are singled out as arts, because they yield products as well as knowledge— direct products of reason, such as grammatical constructions, syllogisms, speeches, enumerations, measurements, melodies, and computed courses of stars. Other sciences either yield no products but only knowledge (e.g. natural science, divine science) and so are not called arts at all, since art according to Aristotle27 is productive reason; or yield bodily products (e.g. medicine, metallurgy, etc.) and so are not called liberal [i.e. free-man] arts, since their activities belong to the body, the servant part of a human being. And though ethics too aims at activity, it aims as Aristotle28 says not at knowing but at acting virtuously; so ethics isn't called an art either, since in such activity virtue substitutes for art. And that is why the ancients defined virtue as the art of living rightly and well, as we read in Augustine.29 to 4: Ibn STná30 points out that the distinction between theoretical and practical means something different in philo sophy, in the arts, and in medicine. In philosophy and the arts the distinction arises from a distinction of goal, the theoretical seeking only knowledge of truth whereas the practical has activity in mind. But philosophy as a whole makes the distinction in a different way from the arts.
For philosophy has regard to the goal of all human life, happiness— as Augustine31 says, quoting Varro, what other reason is there for doing philosophy but to be happy— and so, since philosophers according to Aristotle32 distinguish two kinds of happy life, one contemplative and the other active, they divide philosophy into two, calling ethics prac tical and natural science and logic theoretical. But when the arts are divided into theoretical and practical arts we have regard to goals special to each, calling agriculture practical but dialectic theoretical. As for medicine, its division into
Natural Science, Mathematics, Metaphysics
theoretical and practical doesn't arise from any distinction of goal, for in that respect all medicine is practical, aimed at activity. But the division depends on how closely matters dealt with in medicine relate to that activity; practical medicine teaches healing techniques— what drugs should be prescribed for what disease, for example—while theoretical medicine teaches the deeper principles governing such techniques— the existence of three kinds of 'spirit'33 and umpteen kinds of fever. So calling one part of a practical science theoretical doesn't mean it must be a branch of theoretical science. to 5: There are two ways in which one science can include another: as a part, with a subject-matter which is part of its own (as botany is part of natural science because plants are one group of naturally existing bodies), or as a subordinate, the lower-level science knowing only what is the case and needing the higher-level science to supply the 'why' (as harmony is subordinate to arithmetic). Medicine then is not a part of natural science: its subject-matter is not part of natural science's in the same sense in which it is medicine's, for although the body to be healed is a natural body, it is studied by medicine as healable by artifice, not as healable by nature. Because, however, even in healing by artifice, artifice is at nature's service aiding nature's powers of healing, we must examine natural properties if we are to supply the 'why' of the healing by artifice. So medicine is a subordinate of natural science, just as metallurgy and agriculture are.
That leaves natural science and all its parts theoretical, even if some sciences subordinate to it are practical. to 6: Although the subject-matters of all other sciences are included under being, the subject-matter of metaphysics, it doesn't follow that these other sciences are parts of meta physics. For each of them considers its part of being in a special way distinct from the way metaphysics considers being, so that properly speaking its subject-matter is not part of metaphysics' subject-matter: it is not included under being in the same respect in which being is studied by metaphysics, the respect which makes metaphysics itself a special science
Structures of Thought that can be classified alongside others. What can be called parts of metaphysics in the sense suggested are its treatments of potentiality, actuality, oneness, etc., all of which are con sidered in the same way as metaphysics considers being... to 9: Although divine science is the first of all sciences, our natural approach to it is through the others. As Ibn Slna says34 in order of learning it comes after the natural sciences, which teach many things this science makes use of, such as the generation and decomposition of substances, change, and the like. For the same reason it is learnt after mathematics, for it learns about immaterial substances through numbering and ranking the celestial spheres, and that needs astronomy, which in turn needs all mathematics. And other sciences like music and ethics this science needs if it is to be done well.
This doesn't involve circularity— this science presupposing the conclusions of sciences to which it itself is providing premisses— because a science like natural science doesn't prove what it hands on to first philosophy by premisses derived from first philosophy, but by other self-evident premisses; and in the same way the first philosopher doesn't prove the premisses he hands down to natural science by premisses drawn from it, but by other self-evident premisses.
So there is no circular definition here.
Moreover, the effects which we sense and on which natural science's demonstrations are based start better known to us, but once they have led us to knowledge of their first causes those causes show us the 'why' of the effects which previously showed us the fact of the causes. So natural science has something to offer divine science, yet has its starting-points illuminated by divine science. And this is why
Boethius puts divine science in last place, as last known by us. to 10: Natural science is learnt after mathematics because its generalizations require experience and time, but the objects of its study, because they can be sensed, are naturally better known than mathematical objects abstracted from perceived matter.
Natural Science, Mathematics, Metaphysics
[Article 2] The second question [Is natural philosophy con cerned with changing, material things?] we approach as follows:
It seems natural science is not concerned with changing, material things:
For [1] matter makes things individual. But, as Porphyry35 tells us Plato believed, science is concerned with the general, never with individuals. So natural science is not concerned with material things.
Moreover, [2] science is something in the mind, and the mind knows by abstracting from matter and material conditions.
So you can't have a science of things unabstracted from matter.
Moreover, [3] according to Aristotle36 natural science is con cerned with the ultimate cause of movement, ah ultimate cause which is altogether free from matter. So natural science is not exclusively concerned with material things.
Moreover, [4] science studies what must be so. Now Aristotle37 proves that everything changing, as such, can be or not be so. Of the changing then there can be no science, and thus no natural science.
Moreover, [5] it is not the general that changes: doctors cure particular men, not man in general, as Aristode says.38
Science, however, studies the general case. So natural science can't be about what changes.
Moreover, [6] natural science reaches conclusions about certain unchanging things like the soul39 and the [stationary] earth;40 moreover, as Aristotle41 proves, [when natural things change their forms] the forms as such don't come into and go out of existence, so change only in a derived sense.
Not everything, then, that natural science concerns itself with is changing.
Moreover, [7] all creatures are changeable and only God, as Augustine42 says, unchanging. So if natural science were about changing things it would be about everything, which is clearly false.
Structures of Thought But against that:
[1] natural science studies natural things, things with an interior tendency to move and change. But, as Aristotle43 says, wherever there is change there must be material to change. So natural science is concerned with material, chang ing things.
Moreover, [2] some theoretical science must treat material, changing things; otherwise philosophy, our knowledge of being, would come to us incomplete. But no other science treats such things, neither mathematics nor metaphysics. So it must be natural science.
Moreover, [3] Aristotle leaves us in no doubt about it.44
In reply:
It was the difficulty of this question that forced Plato into postulating his Ideas. Since, as Aristotle45 tells us, he accepted
Cratylus' and Heraclitus' opinion that nothing we sense stays steady, and thought that there could therefore be no sure or scientific knowledge of such things, he postulated certain substances outside the realm of sense which we can know with certainty and define. His mistake lay in confusing what is true of something as such with what is true of it in a derived sense. This fallacy of the derived sense traps many people, even the cleverest, as Aristotle46 says. For within anything we sense, as Aristotle47 has proved, we must dis tinguish the composite thing itself—the whole which comes into and goes out of existence as such—from the form or rule it is exemplifying— which does not come into and go out of existence as such, but only in a derived sense. For it is not house as such that is built, but particular houses. Now things can be considered in abstraction from what does not belong to them as such, so that, considered as such, rules and forms are not what change, though they give form to things that change. So, Aristotle goes on to say, we can have sciences and definitions of them, and, as he proves, in order to have science of what we sense we don't need to know substances outside the realm of sense.
Now these rules that the sciences of things consider are
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considered in abstraction from change, and therefore in abstraction from everything that accompanies change in changing things. Since all change is measured by time, and since no other type of change would exist unless there first was change of place, things, in order to change, must exist in a here and a now. Aijd to do that changing things must be this and that individual by reason of matter having these or those particular dimensions. So the rules which give us scientific knowledge of changing things must be considered in abstraction from this or that particular matter and from anything consequent on matter's particularity; though not in abstraction from the general notion of matter, since the very notion of a rule or form is that of something giving shape to matter. Thus the rule or form of being human, expressed in a definition and providing us with the base for a science, abstracts from these bones and this flesh, but not from bones and flesh as such. And because the individual's rule or form includes this or that matter whereas the general's includes only matter in general, as Aristotle48 says, the type of abstrac tion we are talking of is not said to abstract form from matter as such, but to abstract the general from the particular.
Rules and forms so abstracted can be thought of in two ways: firstly, in themselves, abstracted from change and from this or that matter, and this mode of existence they have only in our minds; and secondly, as rules determining things which are themselves material and changing, starting-points therefore for understanding those things, since all things are known through their forms. So this is how natural science, by way of unchanging rules abstracted from this and that matter, gives us knowledge of the changing material things that exist outside the mind.
Hence: to 1: Only matter having these or those particular dimen sions makes things individual, and even natural science abstracts from matter so considered. to 2: The form of a thing that mind understands is its whatness: as Aristotle49 puts it, the mind's object is the what.
But what a composite thing is in general— a human being.
Structures of Thought for example, or an animal— involves matter in general, though not any particular matter, as Aristotle says.50 So our minds in natural science abstract from this or that matter and any conditions consequent on thisness or thatness but not from matter in general, even if natural scientists con sider such matter only as something formed. So even natural scientists are concerned primarily with form rather than with matter. to 3: Natural science doesn't concern itself with the ultimate cause of movement as if that were part of its subject-matter, but as a limit towards which natural science is led. Now limits don't share the nature of what they limit but relate to it in some way, just as the end-points of lines are not lines but relate to them; and in the same way the ultimate cause of all movement differs in nature from natural things yet relates to them, inasmuch as they move under its influence. So that is the respect under which natural science is concerned with it: not in its own nature but as movement's cause, to 4: A science is about things in two different senses: first and foremost it is about general rules basic to it as that science, but, secondly, it turns back, so to speak, to the things that obey those rules, and uses our bodily powers to apply the rules to particular things that exemplify them. For to the scientist his rule is both an object of knowledge and a means of knowledge. By means of my general rule about what constitutes a human being, I can make judgements about this or that human being. Now general rules don't change, so in that respect all science studies what must be so.
But the things exemplifying the rules sometimes must be how they are unchangingly, and sometimes can be or not be and change; so it is in this respect that we talk of sciences of changing things that can be or not be. to 5: Though the general doesn't change, it expresses a rule about things that do. to 6: Though souls and other natural forms may be unchang ing in themselves, they are involved in change incidentally.
Moreover, as perfections of changing things they fall under natural science. And though the earth as a whole is sta-
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tíonary, that is only true by chance because it already occupies its natural place and is kept there by the same forces that would otherwise move it there; as indeed its parts move to their proper places when away from them. So the earth is subject-matter for natural science, both as a stationary whole and as having parts that move. to 7: The vulnerability to change common to all creatures is not some natural tendency to change, but a dependence on God, without whom, if left to themselves, they would lose hold on existence. That dependence, however, is a subject for metaphysics rather than natural science. And though spiritual creatures can also change by choosing this or that, such change is a subject for divine rather than natural science.
[Article 3] The third question [Does mathematics see the material things it is concerned with in an unchanging and immaterial way?] we approach as follows:
It seems mathematics does not see things that exist in matter in an immaterial way:
For [I] since truth consists in a correspondence of mind to things it must be false to see things other than as they are. So if mathematics sees things that exist in matter immaterially, it will be false, and thus, since science is always of truths, no science.
Moreover, [2] Aristotle51 says a science, in studying its subject-matter, must study every part of its subject-matter.
But matter is a part of anything existing in matter. So a science can't study things existing in matter without studying matter.
Moreover, [3] straight lines constitute a single species. Now mathematics when considering straight lines counts them, talking of three-sided and four-sided figures. So it treats lines as many individuals of one species. But what distinguishes individuals of a common species is their matter, as we saw earlier.52 So mathematicians consider matter.
Moreover, [4] no science that abstracted altogether from matter could argue from material causes. But certain proofs
Structures of Thought in mathematics appeal to causes which can only be material, as when something about a whole is proved from its parts, for, as Aristotle53 says, parts are the material of wholes.
Thus he54 calls the proof that the angle in a semicircle is a right-angle because each part of it is a semi-right-angle a proof by material causes. So mathematics can't abstract from matter altogether.
Moreover, [5] movement can't exist outside of matter. But mathematicians must consider movement, since movements are measured across space intervals, so that the same rules and science are involved in measuring movement as in measuring space, which is mathematics' business. Math ematics then can't altogether refrain from considering matter.
Moreover, [6] astronomy, and the sciences of moving spheres, of weights, and of music, are all parts of mathematics, and in all of them we consider change and changing things.
So mathematics is not entirely abstracted from matter and change.
Moreover, [7] natural science's whole concern is with matter and change. But certain of natural science's conclusions are also conclusions of mathematics, as that the earth is round and at the centre of the universe. So mathematics can't altogether abstract from matter. If you say, it abstracts only from perceived matter, then on the contrary: Perceived matter seems to mean this or that particular matter, since the senses perceive things in their particularity. But all sciences abstract from that, so mathematics shouldn't be called any more abstract than the other sciences...
But against that:
[1] Aristotle says the opposite.55
Moreover, [2] there are things existing in matter into the definition of which matter doesn't enter, as, for example, concavity, which contrasts with snubness in this regard. Now philosophy has to consider everything that exists. So some part of philosophy must consider such things, and in the absence of any other it must be mathematics.
Moreover, [3] what the mind grasps first can be thought without whatever comes along later. Now mathematical
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objects are prior to things in matter and change, which, as Aristotle points out,56 add something to mathematical objects. So mathematics can consider things without con sidering matter and change.
In reply:
For clarity on this point we need to consider how our minds abstract. Now we know that Aristotle57 distinguishes two ways of exercising understanding: so-called simple intuition, knowing what something is; and making connections and disconnections, forming affirmative or negative propositions.
This doubleness in our activity answers to a doubleness in things: for on the one hand a thing has its nature— that which gives what we are understanding a place in the hierarchy of being, whether it be something whole and com plete in itself or a part or a supervening attribute of such a whole; and on the other hand it has its existence—that which in composite things results from the components com ing together, but in non-composite things accompanies the non-composite nature as such.
Now, because truth of understanding is a matter of con forming to how things are, clearly this second way of under standing cannot with truth abstract what in fact is joined, because such abstraction would be saying a disjunction really existed in the thing. Thus, were I to abstract being human from whiteness by saying 'The human being is not white', I would be saying such a disjunction existed in fact; so that if in fact the human being was white my understanding of the situation would be false. This second way of understanding then can abstract with truth only what is disjoined in fact, as when we say 'The human being is not a donkey'.
However, our first way of understanding can abstract what is not in fact disjoined: not in all cases, but in some.
For since, as Aristotle58 says, it is what gives things actuality that makes them understandable, we understand a thing's nature— what it is— either as itself actuality (e.g. non composite substances and forms as such), or through what gives it actuality (as composite substances through their forms), or through something mimicking that role (so that we understand unformed matter as an ability to be formed,
Structures of Thought and empty space as lack of an occupant). In every case we know the nature by what gives it definition. So when what gives definition to a nature and lets us understand it relates to and depends on some other factor, clearly we can't under stand that nature without that other factor. Sometimes the nature and factor are joined— either as part to whole (thus feet can't be understood outside of animals, since what makes feet feet depends on what makes animals animals), or as form to the material it shapes (whether that shaping con stitutes some whole, or merely adds a supervening attribute like snubness, which can't be understood outside of noses); but sometimes the factor is in some separate thing (as with fatherhood, which can't be understood without sonship, though the two relationships belong in different things). If, however, what gives definition to a nature does not depend on some factor, we can abstract it from this factor, under standing one without the other, and this we can do whether they be disjoined in fact (human being and rabbit), or joined as part to whole (letters can be understood separately from their syllable and animals, without their feet, but not vice versa), or joined as form to material or as supervening attri bute to underlying subject (whiteness can be understood separately from being human, and vice versa).
So we have two ways of making distinctions correspond ing to our two ways of understanding things: when making connections and disconnections we distinguish A from B by understanding it to exist outside of B, but when understand ing what things are we distinguish A from B by understand ing what A is without having to understand B at all, whether
B exists joined to A or separate from it. So only the first way of distinguishing things can properly be called 'disjunction'; the second is rightly called 'abstraction', though only if the two things understood apart from one another are in reality joined (understanding animals without understanding stones is not called 'abstracting' animality from stoneness).
So now, since only what is in reality joined can properly speaking be abstracted, we have two sorts of abstraction corresponding to the two sorts of joining just mentioned
(part and whole, form and material), in one of which we
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abstract form from material, and in the other a whole from its parts.
The forms some material takes on can be abstracted from it only if they can be defined independently of it, not if their definition depends on the material. Now every supervening property of a substance is a form that substance takes on, depending on the substance for its definition; so such forms can't be separated from the substance. Nevertheless, such properties supervene on the substance in an order: first comes its muchness [its bulk quantity], then its suchness [its qualities], and then the changes it is susceptible to. As a result substances— the material— can be understood as having muchness before they are understood as having the perceptible qualities which make them into perceptible material. Quantity, therefore, does not depend for its de finition on material-as-perceptible but only on materialas-thinkable: namely, substance without its supervening properties, which is something only thought can comprehend, and to which our senses cannot penetrate. Mathematics is the science of objects abstracted in this way, and considers only quantity in things and whatever accompanies quantity: shapes and the like.
Wholes too cannot be abstracted from every sort of part.
For wholes depend for their definition on certain parts: namely, when being this whole consists precisely in having these components (as syllables need letters, for example, and compounds elements). Such component parts are called specifying or constitutive parts, and a whole cannot be understood without them since they form part of its defini tion. But some parts merely supervene on the whole as such: the two semicircles in a circle, for instance, for how you divide a circle into such parts—-equal or unequal, two or more—is irrelevant to its circularity. This contrasts with a triangle, where the three lines don't supervene but constitute the triangle a triangle. In the same way it is constitutive of human beings that they have reasoning souls and bodies composed of all four elements, and we can't understand human being without such parts: they define being human, as specifying or constitutive parts. But fingers, feet, hands,
Structures of Thought and the like supervene on what we understand being human to be: they do not define being human, and human beings can be understood without them. Whether it has feet or not, whatever is composed of a reasoning soul and a body chemically combining elements in just the way needed to take on a reasoning soul as its form is a human being. Parts that don't define the whole, but are rather defined by it, we call material parts, and all parts in their here-and-now particularity— this soul, that body, this bone, and so on— are related to human being in this way. Such parts are parts essential to Socrates or Plato but not to human being as human being. So from such parts we can abstract the idea of human being, and that is how universals are abstracted from particulars.
The mind then abstracts in two ways. One corresponds to the way form is joined to material or supervening property to underlying subject, and abstracts [mathematical] forms from perceptible material. The other corresponds to the way whole is joined to part, and abstracts universals from par ticulars, abstracting some nature as a whole in its own definiteness abstracted from all non-constitutive, supervening parts.
We don't find the opposite abstractions of parts from wholes or material from its form. For parts are either material parts into whose definition the whole enters, and then they can't be mentally abstracted from the whole; or constitutive parts which can exist outside of their whole, as lines can outside triangles, letters outside syllables, and elements out side compounds, and when things can exist apart we don't use abstraction but disjunction. In the same way we don't talk of abstracting a form from its material if the form gives the material its substance, for such a form and its corresponding material are mutually dependent: they can't be understood without each other since they are the actualiz ing and the potentiality of one and the same thing. Rather we are talking of the supervening form of quantity or shape.
Now material-as-perceptible can't be mentally abstracted from such a form, since we can't understand something having perceptible qualities unless we first understand it to
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have quantity, can't understand colour except in a surface; nor can we think of something as subject to change with out thinking of it as extended. Substance itself, however, material-as-thinkable, can exist without extension; so that to think it without quantity is rather a sort of disjunction than an abstraction.
So we can use our minds to make distinctions in three ways. Firstly, by making connections and disconnections, and this is properly called disjunction and characterizes divine science or metaphysics. Secondly, when articulating what things are, by abstracting form from material-as-perceptible, and this is characteristic of mathematics. And thirdly, when doing the same thing, by abstracting a universal from par ticulars, and this is common to all sciences, even physics, since all sciences lay aside what is irrelevant and attend only to what is essential. It is because certain people didn't under stand how different the last two are from the first that they fell into error, adopting the Pythagorean and Platonist opinion that mathematical objects and universal were things outside the realm of sense.
Hence: to 1: When he abstracts a mathematician doesn't see things other than as they are. For he doesn't think lines exist apart from matter-as-perceptible, but only considers lines and their attributes without considering their perceptible material. His mind hasn't ceased to correspond with things, because even in things a line's nature doesn't depend on what makes material perceptible, but rather the reverse. Obviously then, to quote Aristotle,59 to abstract is not to lie. to 2: The word material is used not only of things of which matter is a part, but also of things existing in matter, and it is in this sense that the lines we perceive are called material.
Now that doesn't prevent lines being understood without matter, for matter-as-perceptible is not part of lines, but a subject in which they exist; and this is the case with surfaces and solid bodies too. For mathematicians don't think of solid bodies as substances, composed of matter and form, but as three-dimensional objects in the genus of quantity, related to
Structures of Thought the body that exists as a substance with physical matter as a part of it, as a supervening property to its subject, to 3: The material in things can't numerically differentiate them unless it itself is first divided into many parts which, by all taking on the same form, become many individuals of the same species. But material can't be so divided unless quantitative extension is presupposed in it, and without that all substances would stay indivisible. So the basic reason for individuality within a common species is quantitative exten sion. Quantitative extension is capable of this because it includes positioning— that is, order of part outside part— as its defining characteristic. As a result, even when quantita tive extension is abstracted from its perceived matter by the mind, we can still imagine numerically different individuals of one species in it, as, for example, several equilateral triangles or several straight lines of the same length. to 4: Mathematics abstracts from matter-as-perceptible but not from all matter. The quantitative parts from which we argue as from material causes are not matter-as-perceptible but parts of matter-as-thought, and that mathematics does consider, as Aristotle points out.60 to 5: Movement isn't of its own nature a quantity, but derives its quantitativeness from elsewhere when we divide movements up by spatial intervals or by division in the things which move. So movement is not part of the subject-matter of mathematics, but mathematical principles apply to it. And so by applying quantitative principles to movement a natural scientist can treat multiplicity and continuity of movement, as Aristode shows.61 And sciences intermediate between mathematics and natural science can measure movement, as in the science of moving spheres and astronomy. to 6: The simple and its attributes exist, transformed, within the complex (for example, the characteristic qualities and movements of the elements are found within compounds), but what is proper to the complex is not found within the simple. As a result the more abstract a science is and the more concerned with the simple, the more its principles can be applied in other sciences. So mathematical principles
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apply to natural things, but not vice versa: it is natural science that adds to mathematics, as Aristotle62 says, and not the reverse. That is why there are three levels of science about natural and mathematical objects: the purely natural sciences concerned with properties of natural things as such: e.g. natural science, agriculture, etc.; the purely mathematical sciences concerned with quantities as such: e.g. geometry with extension and arithmetic with number; and intermediate sciences, applying mathematical principles to natural things: music, astronomy, etc. Because such sciences treat nature as a sort of material underlying a mathematical form, they are nearer to mathematics than natural science: music, for example, considers sounds as numerical ratios rather than sounds, and other sciences do likewise. As a result they prove conclusions about natural things starting from mathematical ideas. Such sciences then share with natural science its study of perceptible matter, but share with mathematics its abstractness. to 7: These intermediate sciences we are discussing consider the same material as natural science but not the same form.
So nothing stops them proving the same conclusions, but not with the same arguments, except in so far as sciences inter penetrate and sometimes use each other's methods. Thus natural science proves the earth round by the way heavy objects move [towards a centre] whilst astronomy proves it by considering [the round shape of] lunar eclipses...
[Article 4] The fourth question [Is divine science concerned with immaterial, unchanging things?] we approach as follows:
It doesn't seem divine science is concerned with things separated off from matter and change:
For [1] divine science seems to be concerned above all with God. But, as Paul in Romans 1 [20] says, God we can come to know only through such effects of his as we can see, because they exist in changing matter. So divine science cannot abstract from matter and change...
Structures of Thought Moreover, [5] divine science— as we are calling the third branch of theoretical science— is identical with metaphysics, the subject-matter of which is being, and principally being-asubstance, as Aristotle makes clear.63 But neither being nor substance abstracts from matter, for then no being could contain matter. So divine science does not abstract from matter.
Moreover, [6] Aristotle64 says a science when considering its subject-matter must consider every part and property of that subject-matter. So since the subject-matter of divine science is being, as we have just said, it must consider anything that is in being. Now there is a sense in which matter and change are in being. So metaphysics must consider them, and divine science cannot abstract from them.
Moreover, [7] Ibn Rushd, commenting on Aristotle's Physics,65 tells us that divine science appeals in its proofs to three kinds of cause: agents, forms, and goals. But, as Aristotle66 has remarked, you can't think agents or goals without thinking change, and mathematics, in its proofs, appeals to neither kind of cause precisely because it studies unchanging objects. So divine science doesn't abstract from change.
Moreover, [8] theology has things to say about the creation of heaven and earth, and human action, and many other things that involve matter and change. So theology, it seems, doesn't abstract from matter and change.
But against that:
[1] Aristotle67 says first philosophy is concerned with things separable (i.e. from matter) and unchanging, and in the same place says first philosophy is divine science. So divine science abstracts from matter and change.
Moreover, [2] the noblest science must deal with the noblest beings. If then divine science is the noblest science, and immaterial, unchanging beings are the noblest beings, divine science must be about them.
Moreover, [3] Aristotle68 says divine science deals with
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ultímate principles and causes. Now these are immaterial and unchanging; so that's what divine science must be about.
In reply:
To be clear on this point consider what science can claim divine status. We know thatevery science must treat the beginnings of its subject-matter, since, as Aristotle69 makes clear, a science is incomplete unless it knows its own beginnings.
Now there are two sorts of beginnings. Some are things complete in their own right, yet originating other things: the heavenly bodies, for example, somehow originate bodies here below, and elements start off compounds. These then science considers in both roles: as beginnings, and as things in them selves; and so they are studied not only in the science con cerned with the things they originate, but also in a separate science devoted to them themselves. Thus a special branch of natural science is devoted to heavenly bodies over and above the branch that deals with bodies here below, and a special branch deals with elements over and above that dealing with compounds. But other sorts of beginning are not things com plete in their own right, but simply the starting-off points for other things, in the way unity starts number off, and points lines, and form and matter the bodies of physics: and such beginnings are treated only in the sciences of the things they start off.
Now just as in any particular genus of being there are beginnings common to everything70 in that genus, so also all beings, because they have being in common, have common beginnings that are the beginnings of all being. Ibn Slná71 says beginnings can be common in two senses: predicably common, in the way what I call form is common to all forms, being predicated of each; and causally common, in the way the one sun originates all life. Now there are begin nings common to all being not only in the first sense—which Aristotle72 calls common to all beings by proportion or analogy— but also in the second sense—since all things take their beginning from a certain fixed number of things, the beginnings of all supervening properties leading back to the beginnings of substances, and the beginnings of perishable
Structures of Thought substances leading back to imperishable substances, and so on up the rungs of a ladder till we are led back to certain beginnings of all beings. And because, as Aristotle73 says, that which begins all being must itself exist the most, such beginnings must themselves be the most perfect and hence the most actual beings, with no or very little potentiality, since, according to Aristotle,74 actual being is prior to and more potent than potential being. They must therefore lack matter, which is a potential to be, and lack change, which is the actualizing of something's potential to be. And such things are divine, since, as Aristotle75 says, if there anywhere exists something divine it must surely be in such a nature, namely, immaterial and unchanging.
These divine things then, because they are at the beginning of all beings and yet are complete things in their own right, we can study in two ways: as the common beginnings of all being, and as things themselves. But because ultimate begin nings, though in themselves most knowable, are present to our minds like the light of the sun to owls' eyes, as Aristotle76 says, our natural light of reason can penetrate to them only by way of their effects: and this, as Romans 1 [20] shows, is the way philosophers penetrated to them: The unseen things of God have been clearly seen by understanding the things he has made. So philosophers treat divine things only as the universal beginnings of things, in that teaching which lays down whatever is common to all beings, having as its subjectmatter being as such; and that is the science they call divine science.
But there is another way of knowing such things, not as their effects reveal them, but as they themselves reveal themselves. And this is the way described by St Paul in 1
Corinthians 2 [11]: No one knows the things of God save the spirit of God. We however have received a spirit not of this world but from God, that we may know; and God has revealed it to us by his spirit. And in this way divine things are treated not simply as the beginnings of other things, but as they subsist in themselves.
So there exist two theologies or divine sciences: in one divine things are not the subject-matter of the science but beginnings of the subject-matter, and this theology philo-
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sophers pursue and also call metaphysics; in the other divine things are considered for themselves as subject-matter of the science, and this theology is the one taught us in holy scripture. Both are about things existing outside matter and change, but in two different ways corresponding to two different senses in which something can exist outside matter and change. In one sense things so exist outside that by definition they cannot exist inside matter and change, and this is the sense in which God and the angels are said to exist outside matter and change; in the other sense things by definition need not exist in matter and change, can exist outside them, but sometimes exist within them, and this is the sense in which being and substance and potentiality and actuality exist outside matter and change, not depending on matter and change for their existence as mathematical objects do, which can exist only within matter although they can be understood abstracted from matter-as-perceptible.
Philosophical theology takes as its subject-matter things out side in this second sense, and treats things outside in the first sense as beginnings of its subject-matter. But the theology of sacred scripture takes as its subject-matter things outside in the first sense, though it treats too of certain changing things existing within matter in so far as the revelation of divine things requires it.
Hence: to 1: Whatever science uses only to illustrate something else is not as such the subject-matter of the science but something extraneous. This is the way natural science uses mathematical ideas, and there is no reason why divine science shouldn't include certain material and changing things in the same way... to 5: Being and substance are said to be outside matter and change, not because they are defined to be outside matter and change (as donkeys are defined to be without reason), but because they are not defined to be inside matter and change, even if sometimes they are (as being animal abstracts from reason even though one type of animal is rational). to 6: A metaphysician considers even individual beings, not as exemplifying this or that type of being, but as sharing
Structures of Thought what all beings have in common; and that is the way he considers even matter and change. to 7: To act and be acted on entities must exist in fact, not just in thought. Now the abstract entities mathematicians think about exist only in thought, so that such entities, mathematically considered, can neither initiate movements nor end them. As a result mathematics doesn't appeal in its proofs to either agents or goals. But the objects divine science thinks about exist separate [from matter] in very fact, able to initiate movements and end them; so there is nothing to stop it using agent and final causality in its proofs. to 8: Just as faith, which disposes us to accept theology's initial premisses, has as object ultimate Truth, though the articles of faith also include other things relating to creatures which touch on ultimate Truth in some way, so theology's principal subject-matter is God, though it touches a great deal on creatures as the effects of God or as relating to him in various other ways.
[Question 6] The next question for debate concerns the dif ferent methods of procedure ascribed to the theoretical sciences, and it raises four points:
Must natural science use reason in its procedures, math ematics discipline, and divine science intellect?
In divine matters should we abandon imagination altogether?
Are our minds able to scrutinize the divine form itself?
Can they do this by way of some theoretical science?
[Article 1] The first question [Must natural science use reason in its procedures, mathematics discipline, and divine science intellect?] we approach as follows:
[Query 1] It doesn't seem that natural science must use reason in its procedures:
For [1] logic is distinct from natural philosophy, and using reason is logic's characteristic. So it would be inappropriate to ascribe it to natural science.
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Moreover, [2] in Aristotle's Physics logical arguments are often distinguished from physical or natural arguments. So using reason or logic is not characteristic of natural science.
Moreover, [3] we shouldn't characterize one science by what is common to all. Now all sciences reason: from effects to causes or from causesto effects or from symptoms. So that shouldn't characterize natural science.
Moreover, [4] Aristotle77 distinguishes what is scientifically true from what is reasonable. Since natural philosophy is scientific we shouldn't characterize it as using reason.
But against that:
[1] We read78 that reason concerns itself with bodily nature, and that is the main subject-matter of natural science. So it seems right to say it uses reason.
Moreover, [2] Boethius79 says reason, by addressing the universal, comprehends what is sense-perceptible and imaginable without using sense-perception or imagination.
Now comprehending the perceptible and imaginable is the work of natural science. So the use of reason is appropriate to it.
Further, [Query 2] it seems inappropriate to say mathematics uses discipline in its procedures:80
For [1] discipline seems to mean scientific learning, and that happens in every branch of philosophy, since philosophy proceeds by proof. So all branches of philosophy use dis cipline, and it shouldn't characterize mathematics.
Moreover, [2] disciplined learning seems easiest when things are most certain. Now the subject-matter of natural science seems more certain than that of mathematics, since we can perceive it with our senses, the source of all our knowledge.
So disciplined learning is more appropriate to natural science than mathematics...
But against that:
[1] To use discipline is to proceed by sure and proven steps.
Now as Ptolemy81 says, Only mathematics, if you examine
Structures of Thought matters closely, builds up in its students sure and stable beliefs by means of irrefutable proofs. So use of discipline is most characteristic of mathematics.
Moreover, [2] Aristotle in several places in his books calls the mathematical sciences disciplines.
Further, [Query 3] using intellect in its procedures doesn't seem appropriate to divine science:
For [1] according to Aristotle82 intellect understands pre misses and science knows conclusions. Now not everything in divine science is premiss, but some of it conclusion. So it is not appropriate to say divine science uses intellect.
Moreover, [2] you cannot use intellect on things which transcend all intellectual understanding. Now pseudoDionysius83 and Aristotle84 both say that divine things transcend intellectual understanding. So they cannot be approached with intellect...
Moreover, [4] theology concerns itself principally with matters of faith, and intellectual understanding is faith's goal, as a textual variant of Isaiah says: 'unless you believe you will not understand'. So intellectual understanding of the divine is a characteristic of theology's goal rather than of its procedures.
But against that:
[1] We read85 that with intellect we know created spirits and with intelligence God himself. But these are the principal subject-matter of divine science, so that use of intellect seems characteristic of that science.
Moreover, [2] the approach of a science should be fitted to its subject-matter. Now things divine are things intellectually understandable of their very nature. The appropriate ap proach for divine science is thus to use intellect.
In reply to Query 1 [Must natural science use reason in its procedures?]:
A procedure of science can be said to use reason in three senses.
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Firstly, because of its starting-point. A proof that bases itself on notions reason has elaborated—logical concepts like
'genus' and 'species' and 'opposite' and suchlike—uses logic or reason in the sense of using logic's teachings, propositions derived from logic, in another science. Such an approach cannot suitably characterize any particular science, which is at fault when it overlooks what is peculiar about its subjectmatter. It is only proper and suitable in logic and meta physics, which are both general sciences, having a sort of shared subject-matter.
In another sense, a procedure can be said to use reason because of its ultimate destination. All reasoned enquiry reaches its ultimate destination when it so understands its starting-point that it can see the truth of its conclusions broken down in that starting-point. A procedure that reaches this destination is called not simply a reasonable proof but a demonstrative [or apodeictic] one. But sometimes reasoned enquiry fails to reach that destination, and comes to a stop when the enquiry is still at a crossroads; that happens when our reasoning is only 'probable', sufficient to ground opinions or belief but not scientific knowledge. Such a procedure we call a reasonable proof rather than a demonstrative one. And any science can use reason in this way, since proofs of a truth's probability prepare the way for proofs of its necessity.
It is yet another way of using logic within the demonstrative sciences, not now logic's teachings but its methods.
In both the senses above reason means the science of reason, for as Ibn Rushd86 points out they are ways we employ logic, the science of reason, in the demonstrative sciences. But there is a third sense of using reason in which reason means our native ability to reason: namely, using reason's characteristic way of knowing things, and such use of reason is characteristic of natural science. For the approach of natural science uses reason's characteristic way of proceeding in two respects. Firstly, just as reason starts from things our senses see, most knowable to us, and comes to know things our intellects see, most knowable in their own natures, so natural science, as Aristotle87 makes clear, starts from what is more knowable to us and less knowable
Structures of Thought in its own nature, using proofs from symptoms and effects.
Secondly, reason characteristically argues from one thing to another, and this is especially typical of natural science, in which we derive knowledge of one thing from knowledge of something external to it—knowledge of effects, for example, from knowledge of their cause— and do not simply argue from one idea of a thing to another idea of the same thing— as when we conclude something about human beings from their being animals. In the mathematical sciences we argue from the definitions of things, proving conclusions by appeal to formal principles, never deriving truths about something by appeal to something external to it but by appeal to its own definition; for even when we prove truths about circles by considering triangles (or vice versa) this is because we find the triangle potentially present in the circle (or vice versa). In natural science, however, there occur proofs from external causes which prove truths about one thing by appeal to another altogether external to it. So this characteristic of reason is especially typical of natural science, and makes natural science more suited to the human mind than any other. Natural science then is said to use reason not because it is the only science to do so, but because that approach is most characteristic of natural science.
Hence: to 1: This argument understands using reason in the first sense, in which it is characteristic of logic and metaphysics but not of natural science. to 2: This argument understands using reason in the second sense. to 3: All sciences reason from one idea to another, but not all reason from one thing to another thing; that is characteristic of natural science and is the sense in which it is said to use reason, as we have said. to 4: At that point Aristotle is identifying the reasonable with opinion, understanding using reason in the second sense above. In the same place he says that about things to be done, the subject-matter of ethics, we can only have reason-
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able opinions, because of their indeterminate nature. So from all that has been said we can gather that in its first sense using reason characterizes logic, in its second ethics, and in its third natural science.
In reply to Query 2 [Must mathematics use discipline in its procedures?]:
Mathematics is said to use discipline in its procedures not because it is the only science to do so, but because the approach is most characteristic of mathematics. Since learn ing means acquiring scientific knowledge from another, a disciplined learning procedure must lead to science, that is, to knowledge which is certain, and this is especially the case in mathematics. For mathematics lies half-way between natural and divine science and is more certain than either.
It is more certain than natural science because it abstracts from matter and change whereas natural science must deal with both. Because it must deal with matter natural scientific knowledge depends on a lot of things: on matter itself, on the forms matter takes on, on the dispositions previously in the matter, and on the properties that result when matter takes on a form. But when knowledge depends on a lot of considerations it is more difficult to acquire: Aristotle88 says that the more abstract sciences are the more certain, arithmetic, for example, more than geometry. Again, because natural science must deal with things in change that behave irregularly, its knowledge is shakier, often predicting what is likely to happen but occasionally happens otherwise.
And this is also why the more involved science becomes in individual cases— as in practical sciences like medicine and metallurgy and ethics—the less certain it becomes: partly because of the many more things such sciences have to con sider if they are not to make mistakes, and partly because those things behave so irregularly.
Mathematical procedure is also more certain than that of divine science, because divine science's subject-matter is further away from what we can sense, where our knowledge starts: whether that subject-matter be immaterial substances about which we are insufficiently informed by what our
Structures of Thought senses tell us, or those attributes all beings have in common which are the most general of attributes and so the furthest removed from the particulars we sense. Mathematical entities like figures, lines, and numbers are things we sense and can imagine, and so the human mind, dependent on images, grasps those entities more easily and certainly than it can immaterial intelligences or even notions like substance or actuality and potentiality, etc.
Clearly then mathematics is easier and more certain than either natural or divine science, and much more so than other practical sciences; and for this reason it above all is said to use discipline in its procedures. And this was what
Ptolemy89 was saying: The other two branches of theoretical science generate opinions rather than scientific notions: theo logy because of its hidden and mysterious subject-matter, physics because its matter is unstable and unclear. Only mathematics builds up in its students sure and stable beliefs by means of irrefutable proofs.
Hence: to 1: As we have said, all branches of science use discipline, but none as easily and certainly as mathematics. to 2: Natural objects are the sort we can perceive with our senses, but because of their fluidity we can't be sure of them unless we are actually perceiving them. But of mathematical objects we can, since they don't change and yet exist in perceptible matter, and so can be both perceived and imagined...
In reply to Query 3 [Must divine science use intellect in its procedures?]:
Just as we say natural science's procedures use reason, because that science above all conforms to reason's way of acting, so we say divine science's procedures use intellect, because that science above all conforms to intellect's way of acting. Reason differs from intellect like the many from the one: or as Boethius90 says: the relation of reason to intellect is like that of time to eternity or a circle to its centre. For the characteristic of reason is to explore many matters and
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simplify them into a single idea. Thus pseudo-Dionysius91 says our minds are rational and fall short of the angels when they wander round exploring truths everywhere, though they match the angels in a sense when they turn the many into one. Intellect, on the other hand, starts with a single simple truth and in considering that finds it knows a whole multi tude of other things, as God by understanding his own being knows everything else. Thus pseudo-Dionysius in the same place says angelic minds are intelligences, because they understand all they can understand of the divine with one and the same idea. Clearly then reason when analysing ends in intelligence, simplifying many things into a single truth, and when synthesizing and discovering begins from intel ligence, where many things are comprehended in one.
So that consideration above all is intellectual, which con cludes all human reasoning. Now the whole of reason's analysis pursued throughout the sciences concludes with the considerations of divine science. For sometimes as we have already said reason argues from one thing to another thing really distinct from it, as when things are proved by appeal ing to their causes or their external effects: synthesizing when we move from cause to effect, analysing in a sense when we move from effects to cause, since causes are simpler and more constant and stably lasting than their effects. And the ultimate conclusion of such analysis in this life is arrival at the simplest supreme causes which are immaterial sub stances. Sometimes, however, reason argues from one idea of a thing to another, as when we argue causes within the thing: synthesizing when we move from the more general to the more detailed,92 analysing when we move the other way, since the more general is simpler. Now what is most general is what is common to all beings; and so the ultimate conclu sion of such analysis in this life is consideration of being as such and everything consequent on it. But these things— immaterial substances and what is common to all being— are the subject-matter of divine science, as we have said. So its considerations are the most intellectual.
It is also for this reason that divine science provides the starting-points for every other science, rational considera-
Structures of Thought tions having their beginning in intellectual ones; and as a result this science is called first philosophy. Nevertheless, because rational considerations have their end in intellectual ones, divine science is learnt after physics and the other sciences; and as a result it is called metaphysics— beyond physics— because analysis leads us to it after physics.
Hence: to 1: We don't say divine science uses intellect as if it didn't reason from premisses to conclusions, but because its reason ing comes closest to intellectual insight, and its conclusions to premisses. to 2: God exceeds the comprehension of all created intellects, but not of uncreated intellect, since he by intellect com prehends himself. But, as regards knowing what he is, he transcends every intellect in this life, though not as regards knowing that he is. And the happiness of the next life con sists in also knowing what he is, seeing his very being. How ever, divine science is not only about God, but about other things that, as regards knowing what they are, do not transcend the human intellect even in this life... to 4: Even knowledge through faith is above all a matter of intellect. For we don't acquire the things we believe by reasoned investigation, but hold to them by a simple consent of intellect. We say we don't understand them because our intellect hasn't full knowledge of them; that is precisely our promised reward.
[Article 2] The second question [In divine matters should we abandon imagination altogether?] we approach as follows:
It seems that in divine matters we ought to have recourse to imagination:
For [1] divine science has never been more ably communicated than in holy scripture. But scripture relies on imagination in divine matters, describing the divine to us in symbols our senses can grasp. In divine matters then we must have recourse to imagination.
Natural Science, Mathematics, Metaphysics
Moreover, [2] only intellect can grasp the divine, which is why we said that in divine science we must use intellect. But, as Aristotle93 says, the intellect can't operate without images.
In divine matters then we must have recourse to imagination.
Moreover, [3] the divine is chiefly revealed through divine illumination. But, as pseudo-Dionysius94 says, the divine light can shine on us from above only if it is shrouded in a variety of sacred veils; and by sacred veils he means senseimagery. In divine matters then we must have recourse to imagination.
Moreover, [4] in dealing with what our senses perceive we must use imagination. But we acquire our knowledge of the divine by way of effects perceived by our senses: as St Paul says in Romans 1 [20], The unseen things of God have been clearly seen by understanding the things he has made.
In divine matters then we must have have recourse to imagination.
Moreover, [5] knowledge must be regulated mostly by the starting-point of that knowledge: in the domain of nature, for example, by the senses where our knowing starts. But our intellectual knowledge starts from imagination, since, as Aristotle95 says, images are to our mind as colours to sight.
In divine matters then we must have recourse to imagination.
Moreover, [6] since mind uses no bodily organ, injury to bodily organs only prevents mental activity in so far as it is has recourse to images. But injury to a bodily organ, namely, the brain, prevents the mind thinking about the divine. So the mind when thinking about the divine is having recourse to imagination.
But against that:
[1] Pseudo-Dionysius96 tells Timothy: Timothy, my friend, to see mysteries you must leave the senses behind. But imagina tion is restricted to what can be sensed, since, as Aristotle97 says, it is a change brought about in us by activity of the senses. So, since it is thinking about the divine that most involves us in mystery, such thinking should not have recourse to imagination.
Structures of Thought Moreover, [2] in any scientific thinking we should avoid what will lead us into mistakes. But, as Augustine98 says, the first mistake in divine matters is trying to apply to the divine what we know to be true of bodily things. Since then imagination is concerned only with the bodily, it would seem that in divine matters we ought not to have recourse to imagination.
Moreover, [3] lesser abilities can't trespass on the speciality of greater abilities, as Boethius99 explains. But we are told100 that knowledge of the divine and the spiritual is the charac teristic of intellect and intelligence. The same authority says that imagination ranks lower than intelligence and intellect, so it would seem that in divine and spiritual matters we ought not to have recourse to imagination.
In reply:
All knowing has a beginning and an end: it begins by taking in information and it ends with the judgement in which it fulfils itself as knowledge. All our knowing begins from sense-perception: what informs the senses informs the imagination— a movement, Aristode says, brought about by the senses— and in us goes on to inform understanding, since what our mind tries to understand is [the world of] our images, as Aristotle101 explains. However, where our know ing ends up is not always the same: sometimes it returns to sense, sometimes to imagination, and sometimes remains in the mind alone.
For when a thing's characteristics and attributes as perceived by our senses adequately express its nature, then our mental judgement of its nature must conform to our sense-perceptions. Everything in nature defined to contain perceptible matter is of this sort, so that natural science's knowing must end up in the senses, making judgements about natural things according to our sense-perceptions of them, as Aristotle102 explains. In nature to neglect senseexperience is to fall into error, where by nature we mean the domain of things containing perceptible matter and subject to change both in fact and in the way we think of them.
But there are other things which we don't judge accord-
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ing to our sense-perceptions, because, though they exist in perceptible matter in reality, they are nevertheless defined abstracting from their perceptible matter; and judgements about anything are most cogent when they accord with how they are defined. But because such things are not defined abstracting from matter in every respect but only from matter as perceptible, and because, when we think away their perceptible qualities, something remains that can be imagined, our judgements of such things must accord with how we imagine them. Such are the objects of mathematics; so in mathematics knowing ends up not in the senses but in imagination, yielding judgements which transcend the information taken in from the senses. This is why judgements about mathematical lines differ on occasion from judgements about lines perceived by the senses: as, for example, that a straight line touches a sphere at a single point, something which Aristotle103 points out is true of straight lines in the abstract but not of straight lines in matter.
There are yet other things which transcend not only the domain of sense but that of imagination as well, namely, things that don't depend on matter at all, either in reality or in our way of thinking about them, the knowing of which ends up in judgements conforming neither to imagination nor to sense-perception. Of course, we come to know such things by way of information that our senses and imagina tion provide, but we submit it to causal argument, deducing from effects causes that incommensurately surpass them, or to processes of transcendence and denial, abstracting from our ideas of such things anything that sense or imagination could take in. These are the ways put forward by pseudoDionysius104 for coming to know the divine from what we sense. Knowledge of the divine, then, can begin with sense and imagination but cannot end there, as it would if we judged the divine to be like the things sense and imagination take in.
Now to have recourse to something is to end up with it. So in divine science we must have recourse neither to sense nor to imagination, in mathematics to imagination but not to sense, but in natural science even to sense. Hence those who
Structures of Thought want to proceed in the same way in all three branches of theoretical science make a big mistake.
Hence: to 1: Holy scripture presents the divine to us in symbols our senses can grasp, not as a place for our mind to rest in, but as a place it can start climbing from, to immaterial things.
For that reason, as pseudo-Dionysius105 says, it presents the divine under even the vilest of symbols, to minimize the chances of our staying attached to them, to 2: In our present state our intellect can't operate without images to start from, but that doesn't mean our knowing must always end up in images, in the sense of judging what we understand to be like what we imagine, to 3: The authority quoted from pseudo-Dionysius describes how our knowing begins, not how it ends.
[to 4:]106 From the effects perceived by our senses we come to our knowledge of the divine in the three ways already mentioned, but this does not force us to make judgements about the divine modelled on how the effects themselves are perceived to be. to 5:107 This argument is valid only when the starting-point of our knowledge is adequate to lead us to what we seek to know, as sense-perception is in the domain of nature but not in divine matters, as we have said. to 6:108 Images are starting-points of our knowing not as starting off our mental activity and then passing away, but as staying there, underlying our mental activity, just as the starting-points of a proof must remain active throughout the deductive process. For images are the objects of our thinking, in which the mind sees what it is looking at either perfectly represented or negated. So when we are prevented from imagining we must needs be prevented from mentally know ing anything, even the divine. For obviously we can't under stand God to cause bodies or surpass all bodies or lack bodiliness if we can't imagine bodies. However, this doesn't conform our judgement of the divine to our imagination. So,
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though in our present life images are necessary if we are to consider divine matters, we must never in such matters have recourse to our imagination.
[Article 3] The third question [Are our minds able to scrutinize the divine forni itself?] we approach as follows:
It doesn't seem we can scrutinize the divine form itself, at least in this life:
For... [2] the divine form is the very substance of God. And since no one can see the very substance of God in this life, no one can scrutinize the divine form itself.
Moreover, [3] to scrutinize the form of a thing is to know it in some way. But pseudo-Dionysius109 says that our mind can best be united with God when it knows absolutely nothing of him. So we cannot scrutinize the divine form.
Moreover, [4] as we have said, all our knowledge begins in the senses. But the things we perceive with the senses cannot adequately reveal to us the form of the divine, nor indeed that of any other immaterial substance. So we can't scrutinize the divine form itself.
But against that:
[1] St Paul in Romans 1 [20] says that the unseen things of God, his eternal power, and his godhead have been clearly seen from the creation of the world, i.e. by man, by under standing the things he has made. But God's form is precisely his godhead. So the very form of God can be known by our understanding in some manner.
Moreover, [2] the gloss110— quoting Gregory— says: Unless a man somehow saw it, namely, the truth of God, he couldn't feel he didn't see it. But we feel we can't perfecdy see the divine substance. So somehow we must see it.
Moreover, [3] pseudo-Dionysius111 tells us that the human spirit learns to expand through what it can see to heights outside this world, which are nothing else than the immaterial forms themselves. So in some way we can know immaterial forms.
Structures of Thought In reply:
There are two ways of knowing: knowing that and knowing what. We know what something is when we understand the essence of it— what makes it what it is—either directly, or [indirectly] by way of something that sufficiently displays what it essentially is. Now during this life our understanding can't directly take in what makes God God or what makes immaterial substances like angels angels, since what we understand directly are images: images are to understanding as colours are to sight, Aristotle112 says. So we can directly conceive what something is when our senses grasp it, but not when only the mind can grasp it. That is why pseudoDionysius113 says we lack ability directly to contemplate the invisible. However, the natures of certain invisible things— what they are— are perfectly expressed in the natures of things sensed as known, and so, indirectly, we can know what such things are. Thus because we know what it is to be human and what it is to be animal the relationship between the two becomes clear enough for us to know what a genus is and what a species. But the natures of things sensed cannot sufficiently express what God is or what immaterial beings are, since these beings are not in the same natural genus; indeed words like 'what' have hardly the same meaning used of things we can see and things we can't. That is why pseudo-Dionysius114 calls analogies for immaterial sub stances drawn from objects we sense unlike likenesses that mean one thing here and another thing there. So analogy from substances we sense can't lead us to know immaterial ones sufficiently well; and neither can causal argument, since any effects such substances produce here below fall short of their causes' full potential and so cannot reveal to us their essential nature.
During this life then we have no way of knowing what these immaterial substances are, either by natural knowledge or by revelation, since, as pseudo-Dionysius115 says, the ray of divine revelation reaches us in our mode. Revelation raises us to know things we otherwise wouldn't, but we don't know them in any other way than through what we sense—
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as pseudo-Dionysius116 says: the divine ray can only enlighten us when veiled around with many sacred veils— and through what we sense we can never reach an adequate knowledge of what immaterial substances are. So we are left not know ing what such immaterial forms are, knowing only that they are, whether we know, this by natural reason's arguments from created effects or by revelation's use of analogies drawn from what we sense.
However, we should note that to know that something exists implies some knowledge of what it is, if not per fect knowledge then at least the kind of vague knowledge
Aristotle117 says we have of what we want to define before we formulate its definition. If you know human beings exist and want to define them you must at least know how the phrase human being is used. And how could you do this unless you had some concept of what you know to exist even though you don't yet know how to define it: a concept composed of certain generic features of human beings, not yet specific enough, and of some of their surface properties.
For knowledge of definitions, like proofs, must base itself on some prior knowledge. So knowing that God or any other immaterial substance exists implies some vague knowledge of what they are.
But now this can't be knowledge of generic features that aren't yet specific enough, since God belongs to no genus, not having what Ibn Sina118 says is requisite for membership of a genus, namely, a what one is added on to one's existence.
And though other created immaterial substances are in genera and share the same broad logical genus of substance with substances we sense, yet they are no more in the same natural genus than heavenly bodies are with earthly bodies: the perishable and the imperishable, as Aristotle119 says, belong to different genera. For logicians consider concepts as such, and they can be applied now to material and perishable things, now to immaterial and imperishable ones; but the natural and divine scientists consider natures as they exist in things, and so where different modes of existence imply different modes of potentiality and actuality they talk of different genera. Furthermore, God has no extrinsic properties,
Structures of Thought as we shall see later, and if other immaterial substances do we don't know them.
So our vague knowledge of immaterial substances can't be based on generic features and surface properties. In such substances generic knowledge is replaced by knowledge through denials, as when we know them to be without matter, without bodies, without shape, etc. The more such denials we make, the less vague our knowledge is, for sub sequent denials make preceding ones more determinate and precise, just as specific differentiations make the broad genus more precise. It is the same way in which we differentiate heavenly bodies from earthly bodies, mostly by denials, affirming, for example, that they are neither light nor heavy, hot nor cold. Again, in the substances we are talking about, knowing surface properties is replaced by knowing their rela tionships to the substances we sense, relationships of cause to effect, or of transcendence.
So then, we know that immaterial forms exist, but instead of knowing what they are we know them through denial, causality, and uplifting, as pseudo-Dionysius120 puts it.
And this is how Boethius understands scrutinizing the divine form itself: not as knowing what God is, but as denying all images.
And this answers all the opposing arguments: the first group which had in mind perfect knowledge of what God is, and those against which had in mind the imperfect knowledge we have just described.
[Article 4] The fourth question [Can they do this (i.e. scru tinize the divine form) by way of some theoretical science?] we approach as follows:
It seems we can come to scrutinize the divine form through some theoretical science:
For... [2] there is a theoretical science which studies immaterial substances, namely, divine science. But a science that studies a substance must scrutinize its form, since we know things through their forms and all proof, as Aristotle121
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says, must start from what a thing is. So we can scrutinize immaterial forms by theoretical sciences.
Moreover, [3] the ultimate happiness of human beings, as philosophy sees it, consists in knowing the immaterial sub stances. For since happiness is whatever activity most fulfils us, it ought, as Aristotle122 suggests, to be concerned with the most perfect objects of intellect. Now the happiness of which philosophers talk is an activity deriving from wisdom, since wisdom is the crowning strength and virtue of our most perfect ability, intellect, and that sort of activity is happiness, as Aristotle123 says. So immaterial substances are understood by wisdom. But wisdom is a branch of speculative science, as we see from Aristotle.124 So we can understand immaterial substances by way of theoretical sciences...
Moreover, [5] everything with a natural goal has built in to it beforehand the ability to attain that goal, and an inclination to pursue it; for natural movements start from within. But human beings have the knowing of immaterial substances as their natural goal, as both philosophers and saints declare.
So they have built in to them by nature the beginnings of that knowledge. But everything we can come to know by naturally known principles falls under some theoretical science. So the knowledge of immaterial substances falls under some theoretical science.
But against that:
[1] Ibn Rushd125 says that to accept this position would imply either that theoretical sciences are not yet perfect since sciences which can understand immaterial substances have not yet been discovered (and this is the alternative if we don't yet understand those substances because of ignorance of some principles), or (if we can't discover such sciences because of some defect in our nature) the implication would be that people who could invent such sciences would be human beings in some quite different sense from ourselves.
The first of these alternatives is improbable and the second impossible. So it cannot be through a theoretical science that we understand such substances.
Structures of Thought Moreover, [2] the theoretical sciences investigate definitions in which the essences of things are understood by dividing up some genus according to differentiating characteristics, and by inquiring into the causes and attributes of things which make a great contribution to knowledge of what the things are. But in the case of immaterial substances we can't know such things, because, as we have said already, they don't belong to the same natural genus as anything we know through the senses; and either, like God, they haven't a cause, or, like angels, their cause is most unclear to us, and their attributes are unknown to us too. So there can't be any theoretical science by way of which we might come to under stand immaterial substances...
Moreover, [3] in the theoretical sciences we know the essences of things through definitions, where a definition is a phrase made up of a genus and differentiating characteristics. But the essences of immaterial substances are non-composite, and no composition enters in to what they are, as Aristotle and Ibn Rushd126 make clear. So we cannot know such sub stances by way of theoretical sciences.
In reply:
In the theoretical sciences we always base ourselves on some thing already known, whether we are proving propositions or discovering definitions. For just as we draw knowledge of a conclusion from propositions previously known, so we come to know a thing's species through concepts of its genus and differentiation and causes. But we can't go on in this way for ever: that would spell the death of all science, its proofs, and its definitions, since you can't bridge the infinite.
So all the considerations of theoretical sciences lead back to certain starting-points that human beings don't have to learn or discover, for then we would have to go on for ever, but have natural knowledge of. These starting-points are the selfevident premisses of proofs to which all proofs lead back, such as that wholes are greater than their parts, and the primary mental conceptions on which all the definitions in such sciences rely, such as being and oneness and so on.
But this shows that theoretical science can know nothing,
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either by proof or by definition, unless it is reachable through these things we know naturally. But what human beings know naturally is what the natural light of our agent intellect makes clear to us, and the only way it can do that is by illuminating our images and making them actually under standable. For that is oar agent intellect's function, according to Aristotle.127 Now images are derived from the senses, so that, as Aristotle128 explains, our knowledge of the startingpoints referred to begins in our senses and our memory. As a result such starting-points cannot lead us outside what we can know from things our senses comprehend.
Now we have already shown that what immaterial sub stances are cannot be known through what we sense, though that such substances exist and have certain features can be known from what we sense. So no theoretical science can lead us to know what immaterial substances are, though theoretical science can prove they exist and show us their intellectuality and imperishability and so on. This also was
Ibn Rushd's129 opinion, though Ibn Bajjah had said the opposite, thinking that what the substances we sense are could adequately express what immaterial substances were.
But, as Ibn Rushd130 says, this is clearly false, for the word what means something almost completely different in the two cases.
Hence:... to 2: Some things we know in themselves, and theoretical science throws light on such things by using their definitions to demonstrate their properties, as in all the sciences which show the 'why' of things. But some things we know not in themselves, but only by way of their effects. And if indeed an effect matches up to its cause, what that effect is can act as a starting-point to prove the cause exists and to enquire into what it is, from which we can then demonstrate its properties as before. But if an effect doesn't match up to its cause, then the effect can serve as a starting-point for proving that the cause exists and has certain features, but what the cause is will always remain unknown; and this is what happens with immaterial substances.
Structures of Thought to 3: The happiness of human beings is twofold. There is an imperfect happiness in this life of which Aristotle is speaking, consisting in the contemplation of immaterial substances to which wisdom disposes us, an imperfect contemplation such as is possible in this life, which does not know what such substances are. The other happiness is the perfect happiness of the next life, when we will see the very substance of God himself and the other immaterial substances. But what brings that happiness won't be any theoretical science, but the light of glory... to 5: There are built in to us beginnings which enable us to prepare for the perfect knowledge of immaterial substances, but don't enable us to attain it. For though human beings are inclined to their ultimate goal by nature, because of the goal's eminence they cannot reach it by nature, but only by God's grace.